Hello there :)
The E7 is an amp + DAC. The E9 is just an amp, but a more powerful one. However, when both are used as an amp only, the E7 is said to be slightly better. If you need explaining on what a DAC and an amp let me know, but apparently you already do.
Yes, if you leave it on it will kill the battery, just like with any electronics. But that doesn't mean the battery's capacity decreases. What I mean is, letting the battery die won't make it die any faster the next time. That only happened with alkaline batteries. With this kind of batteries, that are made of Lithium polymers, they don't have memory. And in fact you should never let it die completely, that is, you should charge it before the battery runs completely out.
And the battery isn't removable.
